"If you find yourself getting lost, geographically, technologically – or psychologically, just give us a call," says the Australian woman in a soothing voice as she straps an iPod to my wrist and plonks an enormous pair of headphones on my head.

We've just met on the street but we've already swapped numbers and now she's giving me directions, telling me to beware slippery cobbles and pressing a pound coin into my palm – to buy myself something nice with. I cross the road, go down some steps, press track one on my iPod and wait, as instructed.

This is en route, a theatrical treasure hunt from the Melbourne company, one step at a time like this, which has already scooped up awards across Australia and now arrives in Edinburgh for its European premiere. As I reach the bottom of the steps, my phone beeps, telling me my next move. For an hour and a half, I am guided around the city by text message – dotting into phone boxes for mystery callers, seeking out directions chalked on the pavement, finding maps tacked to walls and rifling through record shop racks for a brown envelope containing the next set of instructions. Meanwhile, ambient music – all of it composed by local musicians – and random snatches of dialogue play through the headphones.

It's an unsettling, sense-sharpening experience. Led through unfamiliar closes, past washing lines and seedy saunas, through shops and car parks, everyone in the street becomes a potential performer. Is that saxophonist under the bridge part of the performance? Should I say something to that homeless girl? Is that graffiti message meant for me? "Do you traverse the city with your eyes, habit or heart?" intones the iPod. There's quite a lot of this diffuse speechifying but it becomes quite easy to tune out in the thrill of the trail.

I spent the first half hour trying to work out how many people I was being followed by and where they were hiding – they lost me briefly in the rush of Waverley Station and sent a barrage of panicky messages – but eventually paranoia gave way to a kind of euphoria and a breathtaking new perspective on the city.

I'm not quite sure how it counts as theatre but it's enormously good fun and, even as the Edinburgh rain began to lash down for the third time that day, I finished my odyssey oddly moved.